That aside, I went back and replaced the functions and style files with the correct ones from the original child theme to make my website look and function right.

Can I merge the two files style and functions to then include both necesarry code elements to let my theme and bbPress look correct?

It would be stupid to let the bbPress style and funcions overwrite becasue then it would mess up everyones themes. What did you guys do to get it working on a custom theme (i.e. not the one that comes with bbPress).